This paper reviews the authors' recent studies on compressible turbulence by using direct numerical simulation (DNS), including DNS of isotropic (decaying) turbulence, turbulent mixing-layer, turbulent boundary-layer and shock/boundary-layer interaction. Turbulence statistics, compressibility effects, turbulent kinetic energy budget and coherent structures are studied based on the DNS data. The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence
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